Tagged Questions

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Function field Towers of larger depth of recursion

A function field tower is a sequence of function fields $$\mathcal{F}_0 \subset \mathcal{F}_1 \subset \mathcal{F}_2 \dots \subset \mathcal{F}_{n} \subset \mathcal{F}_{n+1} \subset \dots$$ over a base ...
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Isomorphic Algebraic Geometric codes

Let $\chi/\Bbb F_q$ be an algebraic curve over a finite field $\Bbb F_q$ with $q^s$ rational points for some $s\in(0,1)$. Let $L(D)$ be the riemann roch space with prescribed zeros and poles. Let ...
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Are algebraic geometry error correcting codes (Goppa codes) “good” ?

Question (informal version): Are algebraic geometry error correcting codes (V.D. Goppa codes) "good" ? Some details. There is certain construction of error-correcting codes by means of algebraic ...
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How many vectors of Hamming weight L in “random” K dimensional subspace of F_2^N ? Or how good/bad is random linear block code ?

Consider linear $N$-dimensional space $F_2^N$. Consider its $K$ dimensional subspace $V \subset F_2^N$. Let us calculate $w(k,V,N)$ number of vectors in $V$ of Hamming weight $k$ in $V$. Since there ...
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Number of points on a complex sphere with pairwise inner product restriction

Considered the following inner products: $(1)$ $\langle x,y \rangle = \sum_{t=1}^{n}x_{t}y_{t}$ $(2)$ $\langle x,y \rangle_{c} = \sum_{t=1}^{n}x_{t}\bar{y}_{t}$ consider the following surfaces: ...
Lee codes and $n$-torus
This is in continuation with this post: Geometric/Analytic techniques for constructive and asymptotic bounds in the Lee metric Codes over alphabet $\mathbb{Z}_{q}$ of length $n$ for the Lee metric ...